J. Kawakami and J. Murphy, Small and large data scattering for the dispersion-managed NLS. Submitted. [arXiv]

R. Killip, J. Murphy, and M. Visan, Determination of Schrödinger nonlinearities from the scattering map. Submitted.  [arXiv]

A. Ardila, J. Murphy, and J. Zheng, Threshold dynamics for the 3d radial NLS with combined nonlinearity. Submitted. [arXiv]

J. Murphy, A note on averaging and solitons for the dispersion-managed NLS. Nonlinear Differ. Equ. Appl. NoDEA (2024) 31:103.   [arXiv] [Journal]

S. Masaki, J. Murphy, and J. Segata, Global dynamics below excited solitons for the non-radial NLS with potential. Indiana Univ. Math. J. 73 (2024), no. 3, 1097–1205.   [arXiv]  [Journal] [MathSciNet]

A. Ardila and J. Murphy, The cubic-quintic nonlinear Schrödinger equation with inverse-square potential. Nonlinear Differ. Equ. Appl. NoDEA (2024) 31:93.  [arXiv]  [Journal]  [MathSciNet]

L. Campos, J. Murphy, and T. Van Hoose, Averaging for the 2d dispersion-managed NLS. Commun. Contemp. Math. 26, no. 7, Article no. 2350030 (2024). [arXiv]   [Journal] [MathSciNet]

G. Chen and J. Murphy, Recovery of the nonlinearity from the modified scattering map. Int. Math. Res. Not. IMRN 2024, no. 8, 6632–6655.   [arXiv] [Journal]  [MathSciNet]

C. Hogan and J. Murphy, Transmission of fast solitons for the NLS with an external potential. Discrete Contin. Dyn. Syst. 44 (2024), no. 5, 1166–1177.  [arXiv] [Journal] [MathSciNet]

G. Chen and J. Murphy, Stability estimates for the recovery of the nonlinearity from scattering data.  Pure Appl. Anal. 6 (2024), no. 1, 305–317. [arXiv] [Journal] [MathSciNet]

J. Murphy, Recovery of a spatially-dependent coefficient from the NLS scattering map. Comm. Partial Differential Equations 48 (2023), no. 7-8, 991–1007.   [arXiv] [Journal]   [MathSciNet]

L. Campos and J. Murphy, Threshold solutions for the intercritical inhomogeneous NLS. SIAM J. Math. Anal 55 (2023), no. 4, 3807–3843.  [arXiv]  [Journal] [MathSciNet]

A. Ardila and J. Murphy, Threshold solutions for the 3d cubic-quintic NLS. Comm. Partial Differential Equations 48 (2023), no. 5, 819–862.  [arXiv] [Journal] [MathSciNet]

R. Killip. J. Murphy, and M. Visan, The scattering map determines the nonlinearity. Proc. Amer. Math. Soc. 151 (2023), no. 6, 2543–2557. [arXiv] [Journal] [MathSciNet]

J. Murphy and T. Van Hoose, Well-posedness and blowup for the dispersion-managed nonlinear Schrödinger equation. Proc. Amer. Math. Soc. 151 (2023), no. 6, 2489–2502.  [arXiv] [Journal] [MathSciNet]

C. Miao, J. Murphy, and J. Zheng, Threshold scattering for the focusing NLS with a repulsive potential. Indiana Univ. Math. J. 72 (2023), no. 2, 409–453.   [arXiv]  [Journal]  [MathSciNet]

S. Masaki, J. Murphy, and J. Segata, Asymptotic stability of solitary waves for the 1d NLS with an attractive delta potential. Discrete Contin. Dyn. Syst. 43 (2023), no. 6, 2137–2185. [arXiv]  [Journal]   [MathSciNet]

C. Hogan, J. Murphy, and D. Grow, Recovery of a cubic nonlinearity for the nonlinear Schrödinger equation. J. Math. Anal. Appl. 522 (2023), no. 1, Article 127016.  [arXiv]  [Journal]   [MathSciNet]

M. Cardoso, L. G. Farah, C. M. Guzmán, and J. Murphy, Scattering below the ground state for the intercritical non-radial inhomogeneous NLS. Nonlinear Analysis: Real World Applications, Volume 68, 2022, Article 103687.  [arXiv]  [Journal]  [MathSciNet]

J. Murphy, A simple proof of scattering for the intercritical inhomogeneous NLS. Proc. Amer. Math. Soc. 150 (2022), no. 3, 1177–1186.  [arXiv] [Journal]  [MathSciNet]

J. Murphy and T. Van Hoose, Modified scattering for a dispersion-managed nonlinear Schrödinger equation. NoDEA Nonlinear Differential Equations Appl. 29 (2022), no. 1, Art. 1, 11pp.  [arXiv] [Journal]  [MathSciNet]

C. Miao, J. Murphy, and J. Zheng, Scattering for the non-radial inhomogeneous NLS. Math. Res. Lett. 28 (2021), no. 5, 1481–1504.  [arXiv] [Journal]

J. Murphy, A review of modified scattering for the 1d cubic NLS. RIMS Kokyuroku Bessatsu B88 119–146 (2021).  [pdf] [Journal] [MathSciNet]

R. Killip, J. Murphy, and M. Visan, Scattering for the cubic-quintic NLS: crossing the virial threshold. SIAM J. Math. Anal. 53 (2021), no. 5, 5803–5812.  [arXiv] [Journal] [MathSciNet]

J. Murphy, Threshold scattering for the 2d radial cubic-quintic NLS. Comm. Partial Differential Equations 46 (2021), no. 11, 2213–2234.  [arXiv]   [Journal] [MathSciNet]

C. M. Guzmán and J. Murphy, Scattering for the non-radial energy-critical inhomogeneous NLS. J. Differential Equations 295 (2021), 187–210.   [arXiv]   [Journal]  [MathSciNet]

J. Murphy and K. Nakanishi, Failure of scattering to solitary waves for long-range nonlinear Schrödinger equations. Discrete Contin. Dyn. Syst. 41 (2021), no. 3, 1507–1517.  [arXiv] [Journal] [MathSciNet]

B. Dodson, A. Lawrie, D. Mendelson, and J. Murphy, Scattering for defocusing energy subcritical nonlinear wave equations. Anal. PDE 13 (2020), no. 7, 1995–2090.   [arXiv] [Journal]   [MathSciNet]

J. Murphy and Y. Zhang, Numerical simulations for the energy-supercritical nonlinear wave equation. Nonlinearity 33 (2020), no. 11, 6195–6220.  [arXiv] [Journal] [MathSciNet]

R. Killip, J. Murphy, and M. Visan, Invariance of white noise for KdV on the line. Invent. Math. 222, no. 1, 203–282 (2020).   [arXiv] [Journal] [MathSciNet]

S. Masaki, J. Murphy, and J. Segata, Stability of small solitary waves for the 1d NLS with an attractive delta potential. Anal. PDE. 13 (2020), no. 4, 1099–1128.   [arXiv]   [Journal] [MathSciNet]

C. Miao, J. Murphy, and J. Zheng, The energy-critical nonlinear wave equation with an inverse-square potential. Ann. Inst. H. Poincaré Anal. Non Linéaire 37 (2020), no. 2, 417–456.  [arXiv]  [Journal]   [MathSciNet]

A. Arora, B. Dodson, and J. Murphy, Scattering below the ground state for the 2d radial nonlinear Schrödinger equation. Proc. Amer. Math. Soc. 148 (2020), no. 4, 1653–1663.   [arXiv] [Journal] [MathSciNet]

S. Masaki, J. Murphy, and J. Segata, Modified scattering for the one-dimensional cubic NLS with a repulsive delta potential. Int. Math. Res. Not. IMRN 2019, no. 24, 7577–7603.  [arXiv]  [Journal] [MathSciNet]

R. Killip, J. Murphy, and M. Visan, Almost sure scattering for the energy-critical NLS with radial data below H¹(R⁴). Comm. Partial Differential Equations 44 (2019), no. 1, 51–71.  [arXiv]  [Journal] [MathSciNet]

R. Killip, S. Masaki, J. Murphy, and M. Visan, The radial mass-subcritical NLS in negative order Sobolev spaces. Discrete Contin. Dyn. Syst. 39 (2019), no. 1, 553–583.  [arXiv]   [Journal] [MathSciNet]

J. Murphy, Random data final-state problem for the mass-subcritical NLS in L². Proc. Amer. Math. Soc. 147 (2019), no. 1, 339–350.  [arXiv]   [Journal]  [MathSciNet]

J. Murphy, The nonlinear Schrödinger equation with an inverse-square potential. Nonlinear dispersive waves and fluids, 215–225, Contemp. Math. 725 (2019).  [pdf]   [Journal]  [MathSciNet]

B. Dodson and J. Murphy, A new proof of scattering below the ground state for the non-radial focusing NLS. Math. Res. Lett. 25 (2018), no. 6, 1805–1825.   [arXiv]   [Journal]  [MathSciNet]

R. Killip, J. Murphy, and M. Visan, The initial-value problem for the cubic-quintic NLS with non-vanishing boundary conditions. SIAM J. Math. Anal. 50 (2018), no. 3, 2681–2739.  [arXiv]   [Journal] [MathSciNet]

J. Lu, C. Miao, and J. Murphy, Scattering in H¹ for the intercritical NLS with an inverse-square potential. J. Differential Equations 264 (2018), no. 5, 3174–3211.   [arXiv]  [Journal] [MathSciNet]

B. Dodson and J. Murphy, A new proof of scattering below the ground state for the 3d radial focusing cubic NLS. Proc. Amer. Math. Soc. 145 (2017), no. 11, 4859–4867.  [arXiv]  [Journal]  [MathSciNet]

R. Killip, S. Masaki, J. Murphy, and M. Visan, Large data mass-subcritical NLS: critical weighted bounds imply scattering. NoDEA Nonlinear Differential Equations Appl. 24 (2017), no. 4, Art. 38, 33pp.   [arXiv]   [Journal]  [MathSciNet]

J. Murphy and F. Pusateri, Almost global existence for cubic nonlinear Schrödinger equations in one space dimension. Discrete Contin. Dyn. Syst. 37 (2017), 2077–2102.   [arXiv]   [Journal]   [MathSciNet]

R. Killip, J. Murphy, M. Visan, and J. Zheng, The focusing cubic NLS with inverse-square potential in three space dimensions. Differential Integral Equations 30 (2017), no. 3-4, 161–206.   [arXiv]   [Journal]   [MathSciNet]

B. Dodson, C. Miao, J. Murphy, and J. Zheng The defocusing quintic NLS in four space dimensions. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 3, 759–787.   [arXiv]   [Journal]   [MathSciNet]

R. Killip, J. Murphy, and M. Visan, The final-state problem for the cubic-quintic NLS with non-vanishing boundary conditions. Anal. PDE 9 (2016), no. 7, 1523–1574.   [arXiv]  [Journal]  [MathSciNet]  

J. Murphy, The radial defocusing nonlinear Schrödinger equation in three space dimensions. Comm. Partial Differential Equations 40 (2015), no. 2, 265–308.  [arXiv]  [Journal]  [MathSciNet]  

C. Miao, J. Murphy, and J. Zheng, The defocusing energy-supercritical NLS in four space dimensions. J. Funct. Anal. 267 (2014), no. 6, 1662–1724.   [arXiv]  [Journal]  [MathSciNet] 

J. Murphy, The defocusing H^1/2-critical NLS in high dimensions. Discrete Contin. Dyn. Syst. 34 (2014), no. 2, 733–748.   [arXiv]  [Journal]  [MathSciNet]  

J. Murphy, Intercritical NLS: critical H^s-bounds imply scattering. SIAM J. Math. Anal. 46 (2014), no. 1, 939–997.  [arXiv]  [Journal]  [MathSciNet]  

J. Murphy, Nonlinear Schrödinger equations at non-conserved critical regularity. Ph.D. Thesis (2014).   [pdf]  [MathSciNet]